New Fourier Transforms Methods

New fast discrete Fourier Transforms and their adjoints to map a square in space to a disk in the Fourier domain with applications to scientific computations were developed by a team led by Gregory Beylkin at the University of Colorado and George Fann at Oak Ridge National Laboratory. These new methods permit high accuracy computations to and from polar grids. These methods are widely applicable to fast solvers for scientific computations, X-ray tomography, linear inverse scattering, synthetic aperture radar and signal processing. In all of these applications, band-limited functions play an important role.

A special grid on rotating circles in the Fourier domain. This grid is constructed by placing equally spaced nodes (37 in this example) on the circles rotated full 360 degrees around the origin in the same number of steps.

The team is investigating these algorithms for fast computation of scattering kernels in computational chemistry, materials and physics. The application of new grids in Magnetic Resonance Imaging, X-ray tomography and other non-destructive evaluations should result in reduced data collection time as well as improved performance in reconstruction.